CC Geometry H
Aim #7: How do we write equations of perpendicular lines in slope-intercept and
point-slope form?
Do Now: The equations below are in standard form. Put each equation in slopeintercept form. State the slope and y-intercept:
1) 6x + 3y = 12
2) 5x + 7y = 14
3) 2x - 5y = -7
Example: Given A(5,-7) and B(8,2)
a) Find an equation for the line through A and perpendicular to AB in both pointslope and slope-intercept form:
B
A
b) Find an equation for the line through B and perpendicular to AB both point-slope
and slope-intercept form:
B
A
1) Given U(-4,-1) and V(7,1):
a. Write an equation for the line through U and perpendicular to UV in both pointslope and slope-intercept form:
b. Write an equation for the line through V and perpendicular to UV in both pointslope and slope-intercept form:
2) Given S(5,-4) and T(8, 12):
a. Write an equation for the line through S and perpendicular to ST in both pointslope and slope-intercept form:
b. Write an equation for the line through T and perpendicular to ST in both pointslope and slope-intercept form:
3) Given the points R(2,2) and V(3,6), write the equation of the line through R and
perpendicular to RV in both point-slope and slope-intercept form.
4) Given A(-5, -3), B(-1, 6) and C(x, y):
a. What are the coordinates of the translated
points if B moves to the origin?
b. Write the criterion for perpendicularity
equation.
c. Write the equation for BC in slope-intercept form.
5) Given the points C(-3,2) and D(4,4), write the equation of the line through C
and perpendicular to CD in both point-slope and slope-intercept form .
6) Write the equation of a line perpendicular to the line represented by the
equation y = -4x - 7 and that passes through the point (8,-2).
Name_____________________________
Date ____________________
CC Geometry H
HW #7
1. Given points C(-4,3) and D(3,3):
a. Write the equation of the line through
C and perpendicular to CD.
b. Write the equation of the line through
D and perpendicular to CD.
2. Given points N(7, 6) and M(7,-2):
a. Write the equation of the line through
M and perpendicular to MN.
b. Write the equation of the line through
N and perpendicular to MN.
3. A coach is laying out lanes for a race. The lanes are perpendicular to a segment
of the track such that one endpoint of the segment is (2,50) and the other is
(20,65). What are the equations of the lines through the endpoints?
(20,65)
(2,50)
4. Given the points H(-2,-3) and Q(2,-1), write the equation of the line through Q
and perpendicular to HQ.
5. What is the slope of a line perpendicular to the line whose equation is
3x - 7y + 14 = 0.
6. The slope of QR is
state the value of x.
and the slope of ST is
. If
, determine and
Review:
1) Point W is located in plane R . How many distinct lines passing through point W
are perpendicular to plane R ?
2) The diagram below, a right circular cone with a radius of 3 inches has a slant
height of 5 inches, and a right cylinder with a radius of 4 inches has a height of
6 inches. Determine and state the number of full cones of water needed to
completely fill the cylinder with water.